Download Name: Period: ______ Date: Group members: Honors Pre

Name: _____________________________________________________ Period: ________ Date: ___________________
Group members: ____________________________________________________________________________________
Honors Pre-Calculus 2012-13
Ms. York
Chapter 2 Test Review
Directions: Below are questions that will help you prepare for the Chapter 2 Test. There will be a calculator part and a noncalculator part for the test. Try to complete the exercises without a calculator where it states “No Graphing Calculator.”
Section 2.1 – Quadratic Functions (No Graphing Calculator)
1. Find the vertex, axis of symmetry, x-intercepts, and y-intercepts and then sketch a graph of
f (x)  2x 2  12x 16
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2. Among all possible inputs for the function g(x)  3x 2 12x  6 which yields the smallest output? What is this
minimum output?
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3. How far from the origin is the vertex of the parabola y  x 2  6x  13 ?
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4. Find a quadratic function (in vertex-form) for each problem satisfying the given conditions:
a. The graph passes through the origin and the vertex is the center of the circle (x  2) 2  (y  2) 2  16 .
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b. The axis of symmetry is the line x = 1. The y-intercept is 1. There is only one x-intercept.
Section 2.2 – Graphing Polynomials (No Graphing Calculator)
5. What are the characteristics of the graph of a polynomial function?
6. For the following graphs, calculate intercepts, apply leading coefficient test, and use what you know about
multiplicity and its effects are on the graphs.
a. Graph a sketch of the function y  2(x  3) 4 .

1
b. Graph a sketch of the function f (x)  (x  3)(x 1) 3 .
2
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7. Give a reason why the following graphs cannot represent a polynomial function of degree 3.
Section 2.3 – Polynomial Division (Graphing Calculator Okay)
8. Divide out the following expressions:
2x 2  7x  8
a.
x 2
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b.
3x 4  2x 3  2
x 2 1
c.
x 5  a5
xa
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9. When x 3  kx  1 is divided by x  1, the remainder is -4. Find k.
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Section 2.4 – Complex Numbers (Graphing Calculator Okay)
10. Compute the following (answer should be in standard form a + bi)
5  2i
a.
3  4i
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b. (5  6i)  (9  2i)
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11. Let z = 2 + 3i, w = 9 – 4i.
c. Find zw
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___
d. Find z  w

12. i101
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13. Solve: x 2  4 x  6  0
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Section 2.5 – Zeros of polynomials (Graphing Calculator Okay)
14. Find a polynomial equation that satisfies the given conditions. If no such equation is possible, state why.
a. Degree 3; three zeros at 3, -4, 5
b. Degree 3; -2 and -3 are zeros
c. Degree 3; 4 is a zero of multiplicity two; -1 is a zero of multiplicity two
15. Find all zeros of 2x 4  3x 3  12x 2  22x  60 if given that 1 3i is a zero.
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
Section 2.6 – Rational Functions (No Graphing Calculator)
16. Find domain, intercepts, asymptotes, and critical values, and then sketch a graph for each of the following
functions:
3x 15
a. f (x) 
4 x 12
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b. g(x) 
(x 2  4)(x 3 1)
x6
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c.
h(x) 
x2  x  6
x3
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d. t(x) 
x2  9
x3
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Section 2.7 – Nonlinear inequalities (Graphing Calculator Okay)
17. Solve the following inequalities (write answers in interval notation)
a. x 4  14 x 3  48x 2
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
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b.
x3
0
x4
c.
2x 1
2

1
x 1 x  3